 Hi! In this video we'll discuss uniform circular motion. So uniform circular motion is pretty much exactly what it sounds like and it turns out there's lots of objects that undergo this type of motion so if we can understand it then we can model their behavior. Firstly we'll define what exactly uniform circular motion is, then we'll move on to real-life examples of objects undergoing uniform circular motion and finally we'll derive the velocity of an object that's undergoing uniform circular motion. So what is uniform circular motion? While it occurs when an object follows a circular path at a constant or uniform speed. So you can see in the graphic an object that is following a circular path at a constant speed and is therefore undergoing uniform circular motion. There are lots of examples of objects that undergo uniform circular motion or something very close to it. One example that might come to mind is the earth which orbits the sun. One revolution around the sun takes one year or about 365 days. Another example is the moon which orbits the earth and takes about one month to complete one orbit. A third example of an object undergoing uniform circular motion is a tennis ball attached to a string. When the tennis ball is made to swing around a wooden pole it will undergo uniform circular motion. The ball on the string example is similar to lots of other examples you may see of uniform circular motion where an object is attached to a string and is being swung around. You can easily demonstrate this to yourself. Objects traveling along a path on the inferior of a cone can also undergo uniform circular motion if they're traveling at a constant speed. Finally another example is a car on a circular racetrack. If the car is traveling at a constant velocity on a circular racetrack then it is undergoing uniform circular motion. Now we're going to come up with an expression for the velocity of objects undergoing uniform circular motion. So what speed is an object undergoing uniform circular motion actually traveling at? While we know that for a constant velocity the speed v is equal to the distance traveled divided by the time taken to travel that distance. So let's investigate one revolution which is an object traveling once around the circle. We know that the distance the object has traveled is the circumference of the circle. If you remember the circumference of a circle is equal to two pi times the radius of the circle. So for an object undergoing one revolution of the circle the distance is equal to two pi r. Now the time taken to complete one revolution around the circle is the time of the period which we're going to call big t. So for example the period of the earth traveling around the sun which we discussed earlier is 365 days and that's the period of the earth's orbit. So if we look back at our velocity equation and we plug in the values that we've derived we see that v the velocity of an object undergoing uniform circular motion is equal to two pi r the radius of the circle divided by big t the period and there you have it. The speed of an object undergoing uniform circular motion is equal to two pi r on t. So now we know the magnitude of velocity what is the direction of the velocity vector. We know that an object undergoing uniform circular motion is traveling along the circumference of a circle. To undergo this motion the velocity vector of the object must be tangential to the circle at every point. To see this let's consider the velocity of different points along the path of motion. On the top of the circle in our example the object is moving left so the velocity vector must point left. And if we look at the velocity at the bottom of the circle we know that the object must be pointing right so the object is moving rightwards. If we look at the left side of the circle the object is moving downwards so the velocity vector must point down. We can see that at every point on the circle the velocity is pointing tangentially to the circle. So in summary the velocity of the object undergoing uniform circular motion has a magnitude of two pi r on t and the direction of the velocity is tangential to the circle on which the object is undergoing uniform circular motion.